What is (\partial)/(\partial x)((m^2)/(4xy)) ?

The answer to (\partial)/(\partial x)((m^2)/(4xy)) is -(m^2)/(4x^2y)

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(\partial)/(\partial x)((m^2)/(4xy))

\frac{\partial}{\partial x} (\frac{m ^{2}}{4 x y})

- \frac{m ^{2}}{4 x ^{2} y}

Solution steps

\frac{\partial}{\partial x} (\frac{m ^{2}}{4 x y})

Treat

m, y

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{m ^{2}}{4 y} \frac{\partial}{\partial x} (\frac{1}{x})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{m ^{2}}{4 y} \frac{\partial}{\partial x} (x^{- 1})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{m ^{2}}{4 y} (- 1 \cdot x^{- 1 - 1})

Simplify

\frac{m ^{2}}{4 y} (- 1 \cdot x^{- 1 - 1}) : - \frac{m ^{2}}{4 x ^{2} y}

= - \frac{m ^{2}}{4 x ^{2} y}

What is (\partial)/(\partial x)((m^2)/(4xy)) ?
The answer to (\partial)/(\partial x)((m^2)/(4xy)) is -(m^2)/(4x^2y)